Sen. Bernard Sanders, the upstart Democratic candidate for president, said Sunday the U.S. Constitution is “pretty clear” about what should happen when there is a vacancy on the Supreme Court, making the case for President Obama to act swiftly in the wake of Justice Antonin Scalia’s death this weekend.

Mr. Sanders, Vermont independent, said the nation wants a “full contingent” on the high court and that Senate Republicans should drop their plans to stave off any nomination until a new president is in place.

“Let’s get on with that business,” Mr. Sanders told “Fox News Sunday.”

Justice Scalia’s death in Texas erased the high court’s conservative majority and is reshaping the presidential election and Mr. Obama’s final year in office.

Democrats said that with 11 months left in Mr. Obama’s tenure, the Senate has plenty of time to confirm a replacement.

But Republican leaders said Saturday that the Senate should wait until a new president is elected to confirm a replacement.

Mr. Sanders and other Democrats loudly rejected that posture Sunday, saying they have an obligation to follow the Founding Fathers’ constitutional design and fill the court.

“I can’t find a clause that says ‘except when there’s a year left in the term of a Democratic President,’” said Sen. Elizabeth Warren, Massachusetts Democrat.

Mr. Sanders, who is campaigning out West after walloping presumed Democratic front-runner Hillary Clinton in the New Hampshire primary, said though he and Justice Scalia had “very different points of view,” he was a “brilliant” and “colorful” man deserving of respect for his national service.

Turning to the presidential race, Mr. Sanders downplayed the so-called “Clinton firewall,” bolstered by support among minorities, in the primary states that follow Mrs. Clinton’s double-digit loss New Hampshire.

Mr. Sanders said his track record on the economy and criminal reform are compelling to all Americans, including the black and Hispanic voters who are presumed to be in the former secretary of state’s corner.

“I think we’re going to surprise people in Nevada, we’re going to surprise people in South Carolina,” Mr. Sanders said.